Determination of the inhomogeneous preliminary stress-strain state in a piezoelectric disk

The problem of steady radial vibrations of a thin electroelastic hollow disk in a preliminary inhomogeneous plane stress-strain state is solved. Vibrations are caused by a potential difference at the electrodes placed on the end surfaces of the disk. Equations of vibrations and boundary conditions are formulated. The preliminary stress state corresponding to the solution of the Lame problem was investigated. The direct problem of determining the displacement function is solved numerically by the shooting method. The inverse problem of determining the prestress parameter from the change in the natural frequency of the disk is formulated and solved. The accuracy of determining the prestressed state for initial put data specified with an error is analyzed.